Abstract: In this paper we shall be mainly concerned with sequences of orthogonal Laurent polynomials associated with a class of strong Stieltjes distributions introduced by A.S. Ranga. Algebraic properties of certain quadratures formulae exactly integrating Laurent polynomials along with an application to estimate weighted integrals on with nearby singularities are given. Finally, numerical examples involving interpolatory rules whose nodes are zeros of orthogonal Laurent polynomials are also presented.